Problem: A few families took a trip to an amusement park together. Tickets cost $$7.50$ each for adults and $$2.50$ each for kids, and the group paid $$25.00$ in total. There were $2$ fewer adults than kids in the group. Find the number of adults and kids on the trip.
Explanation: Let $x$ equal the number of adults and $y$ equal the number of kids. The system of equations is then: ${7.5x+2.5y = 25}$ ${x = y-2}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${y-2}$ for $x$ in the first equation. ${7.5}{(y-2)}{+ 2.5y = 25}$ Simplify and solve for $y$ $ 7.5y-15 + 2.5y = 25 $ $ 10y-15 = 25 $ $ 10y = 40 $ $ y = \dfrac{40}{10} $ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into ${x = y-2}$ to find $x$ ${x = }{(4)}{ - 2}$ ${x = 2}$ You can also plug ${y = 4}$ into ${7.5x+2.5y = 25}$ and get the same answer for $x$ ${7.5x + 2.5}{(4)}{= 25}$ ${x = 2}$ There were $2$ adults and $4$ kids.